GATE CE 2006

## GATE CE

For a given matrix $$A = \left[ {\matrix{
2 & { - 2} & 3 \cr
{ - 2} & { - 1} & 6 \cr
1 &

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Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ & $$3x+2y=5$$ is

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The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$

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The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $

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Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction)
$$\

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In the design of beams for the limit state of collapse in flexure as per $$IS:$$ $$456$$ - $$2000,$$ let the maximum str

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Consider the following statements:
$$1.\,\,\,\,\,\,$$ The width-to-thickness ratio limitations on the plate elements und

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In the design of beams for the limit state of collapse in flexure as per $$IS:$$ $$456$$ - $$2000,$$ let the maximum str

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Assuming concrete below the neutral axis to be cracked, the shear stress across the depth of a singly-reinforced rectan

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As per $$IS:$$ $$456$$-$$2000,$$ consider the following statements:
$$1.$$ The modular ratio considered in the working s

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In the design of welded tension members, consider the following statements:
$${\rm I}.\,\,\,\,\,\,\,\,\,$$ The entire cr

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Consider the following statements
$${\rm I}.\,\,\,\,$$ Effective length of a battened column is usually increased to acc

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Mohr's cicle for the state of stress defined by $$\left[ {\matrix{
{30} & 0 \cr
0 & {30} \cr
} } \ri

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A simply supported beam $$AB$$ has the bending moment diagram as shown in the following figure :
The beam is possibly

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A long shaft of diameter $$d$$ is subjected to twisting moment $$T$$ at its ends. The maximum normal stress acting at i

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$${\rm I}$$-section of a beam is formed by gluing wooden planks as shown in the figure below. If this beam transmits a

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A beam with cross-section given below is subjected to a positive bending moment (causing compression at the top) of $$16

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For the section shown below, second moment of the area about an axis $$d/4$$ distance above the bottom of the area is

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Consider the beam $$AB$$ shown in the figure below. Part $$AC$$ of the beam is rigid while Part $$CB$$ has the flexural

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A thin-walled long cylindrical tank of inside radius $$'r'$$ is subjected simultaneously to internal gas pressure $$P$$

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The buckling load $$P = {P_{cr}}$$ for the column $$AB$$ in figure, as $${K_T}$$ approaches infinity, becomes $$\alpha {

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Consider a propped cantilever $$ABC$$ under two loads of magnitude $$P$$ each as shown in figure below. Flexural rigidit

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Consider a propped cantilever $$ABC$$ under two loads of magnitude $$P$$ each as shown in figure below. Flexural rigidit

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Consider the beam $$ABCD$$ and the influence line as shown below. The influence line pertains to

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Vertical reaction developed at $$B$$ in the frame below due to the applied load of $$100$$ $$kN$$ (with $$150,000$$ $$m{

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Carry-over factor $${C_{AB}}$$ for the beam shown in the figure below is

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When the triangular section of a beam as shown below becomes a plastic hinge, the compressive force acting on the sectio

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